Problem: Solve for $x$ and $y$ using elimination. ${-2x+2y = -14}$ ${5x-2y = 44}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $3x = 30$ $\dfrac{3x}{{3}} = \dfrac{30}{{3}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-2x+2y = -14}\thinspace$ to find $y$ ${-2}{(10)}{ + 2y = -14}$ $-20+2y = -14$ $-20{+20} + 2y = -14{+20}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 10}$ into $\thinspace {5x-2y = 44}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ - 2y = 44}$ ${y = 3}$